arXiv subjects

Dibyendu Das

Publications and source records attributed to Dibyendu Das.

At least 37 records · Page 2Linked to original sources

arXiv2022

First passage in the presence of stochastic resetting and a potential barrier

Diffusion and first passage in the presence of stochastic resetting and potential bias have been of recent interest. We study a few models, systematically progressing in their complexity, to understand the usefulness of resetting. In the parameter space of the models, there are multiple continuous and discontinuous transitions where the advantage of resetting vanishes. We show these results analytically exactly for a tent-potential, and numerically accurately for a quartic-potential relevant to a magnetic system at low temperatures. We find that the spatial asymmetry of the potential across the barrier, and the number of absorbing boundaries, play a crucial role in determining the type of transition.

cond-mat.stat-mech↗

arXiv2020

Capture of a diffusive prey by multiple predators in confined space

The first passage search of a diffusing target (prey) by multiple searchers (predators) in confinement is an important problem in the stochastic process literature. While the analogous problem in open space has been studied in some details, a systematic study in confined space is still lacking. In this paper, we study the first passage times for this problem in 1,2 and $3-$dimensions. Due to confinement, the survival probability of the target takes a form $\sim e^{-t/τ}$ at large times $t$. The characteristic capture timescale $τ$ associated with the rare capture events are rather challenging to measure. We use a computational algorithm that allows us to estimate $τ$ with high accuracy. We study in details the behavior of $τ$ as a function of the system parameters, namely, the number of searchers $N$, the relative diffusivity $r$ of the target with respect to the searcher, and the system size. We find that $τ$ deviates from the $\sim 1/N$ scaling seen in the case of a static target, and this deviation varies continuously with $r$ and the spatial dimensions.

cond-mat.stat-mech↗

arXiv2020

Role of dimensions in first passage of a diffusing particle under stochastic resetting and attractive bias

Recent studies in one dimension have revealed that the temporal advantage rendered by stochastic resetting to diffusing particles in attaining first passage, may be annulled by a sufficiently strong attractive potential. We extend the results to higher dimensions. For a diffusing particle in an attractive potential $V({R})=k {R}^n$, in general $d$ dimensions, we study the critical strength $k = k_c$ above which resetting becomes disadvantageous. The point of continuous transition may be exactly found even in cases where the problem with resetting is not solvable, provided the first two moments of the problem without resetting are known. We find the dimensionless critical strength $κ_{c,n}(k_c)$ exactly when $d/n$ and $2/n$ take positive integral values. Also for the limiting case of a box potential (representing $n \to \infty$), and the special case of a logarithmic potential $k \ln\big(\frac{R}{a}\big)$, we find the corresponding transition points $κ_{c,\infty}$ and $κ_{c,l}$ exactly for any dimension $d$. The asymptotic forms of the critical strengths at large dimensions $d$ are interesting. We show that for the power law potential, for any $n \in (0,\infty)$, the dimensionless critical strength $κ_{c,n} \sim d^{\frac{1}{n}}$ at large $d$. For the box potential, asymptotically, $κ_{c,\infty} \sim (1 - \ln(\frac{d}{2})/d)$, while for the logarithmic potential, $κ_{c,l} \sim d$.

cond-mat.soft↗

arXiv2019

Deep Learning-based Hybrid Graph-Coloring Algorithm for Register Allocation

Register allocation, which is a crucial phase of a good optimizing compiler, relies on graph coloring. Hence, an efficient graph coloring algorithm is of paramount importance. In this work we try to learn a good heuristic for coloring interference graphs that are used in the register allocation phase. We aim to handle moderate sized interference graphs which have 100 nodes or less. For such graphs we can get the optimal allocation of colors to the nodes. Such optimal coloring is then used to train our Deep Learning network which is based on several layers of LSTM that output a color for each node of the graph. However, the current network may allocate the same color to the nodes connected by an edge resulting in an invalid coloring of the interference graph. Since it is difficult to encode constraints in an LSTM to avoid invalid coloring, we augment our deep learning network with a color correction phase that runs after the colors have been allocated by the network. Thus, our algorithm is hybrid in nature consisting of a mix of a deep learning algorithm followed by a more traditional correction phase. We have trained our network using several thousand random graphs of varying sparsity. On application of our hybrid algorithm to various popular graphs found in literature we see that our algorithm does very well when compared to the optimal coloring of these graphs. We have also run our algorithm against LLVMs popular greedy register allocator for several SPEC CPU 2017 benchmarks and notice that the hybrid algorithm performs on par or better than such a well-tuned allocator for most of these benchmarks.

cs.LG↗

arXiv2019

Coarsening Dynamics in the Vicsek Model of Active Matter

We study the flocking model introduced by Vicsek in the "coarsening" regime. At standard self-propulsion speeds, we find two distinct growth laws for the coupled density and velocity fields. The characteristic length scale of the density domains grows as $L_ρ(t) \sim t^{θ_ρ}$ (with $θ_ρ\simeq 0.25$), while the velocity length scale grows much faster, $viz.$, $L_{v}(t) \sim t^{θ_v}$ (with $θ_v \simeq 0.83$). The spatial fluctuations in the density and velocity fields are studied by calculating the two-point correlation function and the structure factor, which show deviations from the well-known Porod's law. This is a natural consequence of scattering from irregular morphologies that dynamically arise in the system. At large values of the scaled wave-vector, the scaled structure factors for the density and velocity fields decay with powers $-2.6$ and $-1.52$, respectively.

cond-mat.soft↗

arXiv2019

Velocity distribution of driven granular gases

The granular gas is a paradigm for understanding the effects of inelastic interactions in granular materials. Kinetic theory provides a general theoretical framework for describing the granular gas. Its central result is that the tail of the velocity distribution of a driven granular gas is a stretched exponential that, counterintuitively, decays slower than that of the corresponding elastic gas in equilibrium. However, a derivation of this result starting from a microscopic model is lacking. Here, we obtain analytical results for a microscopic model for a granular gas where particles with two-dimensional velocities are driven homogeneously and isotropically by reducing the velocities by a factor and adding a stochastic noise. We find two universal regimes. For generic physically relevant driving, we find that the tail of the velocity distribution is a Gaussian with additional logarithmic corrections. Thus, the velocity distribution decays faster than the corresponding equilibrium gas. The second universal regime is less generic and corresponds to the scenario described by kinetic theory. Here, the velocity distribution is shown to decay as an exponential with additional logarithmic corrections, in contradiction to the predictions of the phenomenological kinetic theory, necessitating a re-examination of its basic assumptions.

cond-mat.stat-mech↗

arXiv2019

First passage of a particle in a potential under stochastic resetting: a vanishing transition of optimal resetting rate

First passage in a stochastic process may be influenced by the presence of an external confining potential, as well as "stochastic resetting" in which the process is repeatedly reset back to its initial position. Here we study the interplay between these two strategies, for a diffusing particle in an one-dimensional trapping potential $V(x)$, being randomly reset at a constant rate $r$. Stochastic resetting has been of great interest as it is known to provide an "optimal rate" ($r_*$) at which the mean first passage time is a minimum. On the other hand an attractive potential also assists in first capture process. Interestingly, we find that for a sufficiently strong external potential, the advantageous optimal resetting rate vanishes (i.e. $r_*\to 0$). We derive a condition for this $optimal$ $resetting$ $rate$ $vanishing$ $transition$, which is continuous. We study this problem for various functional forms of $V(x)$, some analytically, and the rest numerically. We find that the optimal rate $r_*$ vanishes with the deviation from critical strength of the potential as a power law with an exponent $β$ which appears to be universal.

cond-mat.soft↗

arXiv2017

Shock propagation in locally driven granular systems

We study shock propagation in a system of initially stationary hard-spheres that is driven by a continuous injection of particles at the origin. The disturbance created by the injection of energy spreads radially outwards through collision between particles. Using scaling arguments, we determine the exponent characterizing the power law growth of this disturbance in all dimensions. The scaling functions describing the various physical quantities are determined using large scale event driven simulations in two and three dimensions for both the elastic and the inelastic system. The results are shown to describe well the data from two different experiments on granular systems that are similarly driven.

cond-mat.stat-mech↗

arXiv2017

Diffusion dynamics and steady states of systems of hard rods on the square lattice

It is known from grand canonical simulations of a system of hard rods on two dimensional lattices that an orientationally ordered nematic phase exists only when the length of the rods is at least seven. However, a recent microcanonical simulation with diffusion kinetics, conserving both total density and zero nematic order, reported the existence of a nematically phase segregated steady state with interfaces in the diagonal direction for rods of length six [Phys. Rev. E 95, 052130 (2017)], violating the equivalence of different ensembles for systems in equilibrium. We resolve this inconsistency by demonstrating that the kinetics violate detailed balance condition and drives the system to a nonequilibrium steady state. By implementing diffusion kinetics that drives the system to equilibrium, even within this constrained ensemble, we recover earlier results showing phase segregation only for rods of length greater than or equal to seven. Furthermore, in contrast to the nonequilibrium steady state, the interface has no preferred orientational direction. In addition, by implementing different nonequilibrium kinetics, we show that the interface between the phase segregated states can lie in different directions depending on the choice of kinetics.

cond-mat.soft↗

arXiv2017

Velocity Distribution of Driven Inelastic One-component Maxwell gas

The nature of the velocity distribution of a driven granular gas, though well studied, is unknown as to whether it is universal or not, and if universal what it is. We determine the tails of the steady state velocity distribution of a driven inelastic Maxwell gas, which is a simple model of a granular gas where the rate of collision between particles is independent of the separation as well as the relative velocity. We show that the steady state velocity distribution is non-universal and depends strongly on the nature of driving. The asymptotic behavior of the velocity distribution are shown to be identical to that of a non-interacting model where the collisions between particles are ignored. For diffusive driving, where collisions with the wall are modelled by an additive noise, the tails of the velocity distribution is universal only if the noise distribution decays faster than exponential.

cond-mat.stat-mech↗

arXiv2016

Sufficient conditions for the additivity of stall forces generated by multiple filaments or motors

Molecular motors and cytoskeletal filaments work collectively most of the time under opposing forces. This opposing force may be due to cargo carried by motors or resistance coming from the cell membrane pressing against the cytoskeletal filaments. Some recent studies have shown that the collective maximum force (stall force) generated by multiple cytoskeletal filaments or molecular motors may not always be just a simple sum of the stall forces of the individual filaments or motors. To understand this excess or deficit in the collective force, we study a broad class of models of both cytoskeletal filaments and molecular motors. We argue that the stall force generated by a group of filaments or motors is additive, that is, the stall force of $N$ number of filaments (motors) is $N$ times the stall force of one filament (motor), when the system is in equilibrium at stall. Conversely, we show that this additive property typically does not hold true when the system is not at equilibrium at stall. We thus present a novel and unified understanding of the existing models exhibiting such non-addivity, and generalise our arguments by developing new models that demonstrate this phenomena. We also propose a quantity similar to thermodynamic efficiency to easily predict this deviation from stall-force additivity for filament and motor collectives.

cond-mat.soft↗

arXiv2016

Coherent motion of monolayer sheets under confinement and its pathological implications

Coherent angular rotation of epithelial cells is thought to contribute to many vital physiological processes including tissue morphogenesis and glandular formation. However, factors regulating this motion, and the implications of this motion if perturbed remain incompletely understood. In the current study, we address these questions using a cell-center based model in which cells are polarized, motile, and interact with the neighboring cells via harmonic forces. We demonstrate that, a simple evolution rule in which the polarization of any cell tends to orient with its velocity vector can induce coherent motion in geometrically confined environments. In addition to recapitulating coherent rotational motion observed in experiments, our results also show the presence of radial movements and tissue behavior that can vary between solid-like and fluid-like. We show that the pattern of coherent motion is dictated by the combination of different physical parameters including number density, cell motility, system size, bulk cell stiffness and stiffness of cell-cell adhesions. We further observe that, perturbations in the form of cell division can induce a reversal in the direction of motion when cell division occurs synchronously. Moreover, when the confinement is removed, we see that the existing coherent motion leads to cell scattering, with bulk cell stiffness and stiffness of cell-cell contacts dictating the invasion pattern. In summary, our study provides an in-depth understanding of the origin of coherent rotation in confined tissues, and extracts useful insights into the influence of various physical parameters on the pattern of such movements

q-bio.CB↗

arXiv2014

Inhomogeneous Cooling of the Rough Granular Gas in Two Dimensions

We study the inhomogeneous clustered regime of a freely cooling granular gas of rough particles in two dimensions using large-scale event driven simulations and scaling arguments. During collisions, rough particles dissipate energy in both the normal and tangential directions of collision. In the inhomogeneous regime, translational kinetic energy and the rotational energy decay with time $t$ as power-laws $t^{-θ_T}$ and $t^{-θ_R}$. We numerically determine $θ_T \approx 1$ and $θ_R \approx 1.6$, independent of the coefficients of restitution. The inhomogeneous regime of the granular gas has been argued to be describable by the ballistic aggregation problem, where particles coalesce on contact. Using scaling arguments, we predict $θ_T=1$ and $θ_R=1$ for ballistic aggregation, $θ_R$ being different from that obtained for the rough granular gas. Simulations of ballistic aggregation with rotational degrees of freedom are consistent with these exponents.

cond-mat.soft↗

arXiv2014

Collective force generated by multiple biofilaments can exceed the sum of forces due to individual ones

Collective dynamics and force generation by cytoskeletal filaments are crucial in many cellular processes. Investigating growth dynamics of a bundle of N independent cytoskeletal filaments pushing against a wall, we show that chemical switching (ATP/GTP hydrolysis) leads to a collective phenomenon that is currently unknown. Obtaining force-velocity relations for different models that capture chemical switching, we show, analytically and numerically, that the collective stall force of N filaments is greater than N times the stall force of a single filament. Employing an exactly solvable toy model, we analytically prove the above result for N=2. We, further, numerically show the existence of this collective phenomenon, for N>=2, in realistic models (with random and sequential hydrolysis) that simulate actin and microtubule bundle growth. We make quantitative predictions for the excess forces, and argue that this collective effect is related to the non-equilibrium nature of chemical switching.

physics.bio-ph↗

arXiv2014

Force-induced dynamical properties of multiple cytoskeletal filaments are distinct from that of single filaments

How cytoskeletal filaments collectively undergo growth and shrinkage is an intriguing question. Collective properties of multiple bio-filaments (actin or microtubules) undergoing hydrolysis, have not been studied extensively earlier, within simple theoretical frameworks. In this paper, we show that collective properties of multiple filaments under force are very distinct from the properties of a single filament under similar conditions -- these distinctions manifest as follows: (i) the collapse time during collective catastrophe for a multifilament system is much larger than that of a single filament with the same average length, (ii) force-dependence of the cap-size distribution of multiple filaments are quantitatively different from that of single filament, (iii) the diffusion constant associated with the system length fluctuations is distinct for multiple filaments, (iv) switching dynamics of multiple filaments between capped and uncapped states and the fluctuations therein are also distinct. We build a unified picture by establishing interconnections among all these collective phenomena. Additionally, we show that the collapse times during catastrophes can be sharp indicators of collective stall forces exceeding the additive contributions of single filaments.

physics.bio-ph↗

arXiv2013

Energy decay in three-dimensional freely cooling granular gas

The kinetic energy of a freely cooling granular gas decreases as a power law $t^{-θ}$ at large times $t$. Two theoretical conjectures exist for the exponent $θ$. One based on ballistic aggregation of compact spherical aggregates predicts $θ= 2d/(d+2)$ in $d$ dimensions. The other based on Burgers equation describing anisotropic, extended clusters predicts $θ=d/2$ when $2\le d \le 4$. We do extensive simulations in three dimensions to find that while $θ$ is as predicted by ballistic aggregation, the cluster statistics and velocity distribution differ from it. Thus, the freely cooling granular gas fits to neither the ballistic aggregation or a Burgers equation description.

cond-mat.soft↗

arXiv2012

Giant number fluctuations in microbial ecologies

Statistical fluctuations in population sizes of microbes may be quite large depending on the nature of their underlying stochastic dynamics. For example, the variance of the population size of a microbe undergoing a pure birth process with unlimited resources is proportional to the square of its mean. We refer to such large fluctuations, with the variance growing as square of the mean, as Giant Number Fluctuations (GNF). Luria and Delbruck showed that spontaneous mutation processes in microbial populations exhibit GNF. We explore whether GNF can arise in other microbial ecologies. We study certain simple ecological models evolving via stochastic processes: (i) bi-directional mutation, (ii) lysis-lysogeny of bacteria by bacteriophage, and (iii) horizontal gene transfer (HGT). For the case of bi-directional mutation process, we show analytically exactly that the GNF relationship holds at large times. For the ecological model of bacteria undergoing lysis or lysogeny under viral infection, we show that if the viral population can be experimentally manipulated to stay quasi-stationary, the process of lysogeny maps essentially to one-way mutation process and hence the GNF property of the lysogens follows. Finally, we show that even the process of HGT may map to the mutation process at large times, and thereby exhibits GNF.

q-bio.PE↗

arXiv2012

Broad-tailed force distributions and velocity ordering in a heterogeneous membrane model for collective cell migration

Correlated velocity patterns and associated large length-scale transmission of traction forces have been observed in collective live cell migration as a response to a "wound". We argue that a simple physical model of a force-driven heterogeneous elastic membrane sliding over a viscous substrate can qualitatively explain a few experimentally observed facts: (i) the growth of velocity ordering which spreads from the wound boundary to the interior, (ii) the exponential tails of the traction force distributions, and (iii) the swirling pattern of velocities in the interior of the tissue.

physics.bio-ph↗